Question

How much would you need to deposit in an account now in order to have $2000 in the account in 10 years?

Assume the account earns 4% interest compounded annually. Round your answer to the nearest cent.

Answer 1

To have $2,000 in an account in 10 years at a 4% annual interest rate compounded annually, you need to deposit $1,351.35 now. The calculation uses the compound interest formula for present value.

Step-by-step explanation:

To find out how much money you need to deposit now to have $2,000 in an account in 10 years with an annual interest rate of 4% compounded annually, you can use the formula for the present value of a future sum in compound interest, which is:

PV = FV / (1 + r)^n

Where:

• PV = Present Value (the amount of money you need to deposit now)
• FV = Future Value (the amount of money you want in the future, here $2,000)
• r = annual interest rate (here 4%, or 0.04)
• n = number of years (here 10)

Plugging the values into the formula gives us:

PV = $2,000 / (1 + 0.04)^10

PV = $2,000 / (1.04)^10

PV = $2,000 / 1.48024

PV = $1,351.35

Therefore, you need to deposit $1,351.35 into the account now to have $2,000 in 10 years at a 4% annual interest rate, compounded annually.